Super-resolution Optical Fluctuation Imaging -- fundamental estimation theory perspective

TL;DR

This paper provides a fundamental theoretical analysis of super-resolution optical fluctuation imaging (SOFI), establishing resolution limits based on estimation theory and benchmarking current methods under practical constraints.

Contribution

It introduces a resolution gain metric linked to estimation theory and derives fundamental resolution limits scaling with the fourth-root of source luminosity.

Findings

Resolution limits scale at most as the fourth-root of mean luminosity.

Benchmarking shows performance of SOFI methods under limited photon counts.

Operational resolution gain metric connects estimation theory with imaging practice.

Abstract

We provide a quantitative analysis of super-resolution imaging techniques which exploit temporal fluctuations of luminosity of the sources in order to beat the Rayleigh limit. We define an operationally justified resolution gain figure of merit, that allows us to connect the estimation theory concepts with the ones typically used in the imaging community, and derive fundamental resolution limits that scale at most as the fourth-root of the mean luminosity of the sources. We fine-tune and benchmark the performance of state-of-the-art methods, focusing on the cumulant-based image processing techniques (known under the common acronym SOFI), taking into account the impact of limited photon number and sampling time.